Best Known (139−56, 139, s)-Nets in Base 5
(139−56, 139, 252)-Net over F5 — Constructive and digital
Digital (83, 139, 252)-net over F5, using
- 7 times m-reduction [i] based on digital (83, 146, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 73, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- trace code for nets [i] based on digital (10, 73, 126)-net over F25, using
(139−56, 139, 292)-Net over F5 — Digital
Digital (83, 139, 292)-net over F5, using
(139−56, 139, 8313)-Net in Base 5 — Upper bound on s
There is no (83, 139, 8314)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 14 392624 760885 881940 562049 968126 438369 912823 682897 675824 544945 957189 878577 379734 898460 757813 295297 > 5139 [i]